CN106896351A - A kind of radar network composite Poewr control method based on non-cooperative game - Google Patents

Abstract

The invention discloses a kind of radar network composite Poewr control method based on non-cooperative game, belong to Radar Signal Processing Technology field.This method is according to priori, the RCS of propagation loss and target relative to each radar in acquisition system between each radar and target；Then, under conditions of certain target acquisition performance is met, radar transmission power is minimized, sets up the radar network composite Power control model based on non-cooperative game, and model is solved by classical Lagrangian Relaxation Algorithm.Through iterative calculation, it is chosen at and meets under target acquisition performance condition so that the minimum performance number of each radar transmission powerAs optimal solution, you can obtain meeting the Radar Network System minimum total emission power of constraints.The present invention had both reduced the interference between different radars in Radar Network System, while improve the radio frequency Stealth Fighter of system in the case where certain target acquisition performance is met.

Description

Radar networking power control method based on non-cooperative game

Technical Field

The invention relates to a radar networking power control method based on a non-cooperative game, and belongs to the technical field of radar signal processing.

Background

The radar networking system is a comprehensive integrated electronic information system which is formed by connecting a plurality of transmitters, receivers and a network central station which are dispersedly deployed at different places into an organic whole through a specific network protocol and equipment, realizes the cooperative work of a time domain, a frequency domain and a space domain, and completes the functions of target reconnaissance, detection, information collection, identification and tracking, firepower guidance and the like.

However, with the increasing complexity of today's battlefield electromagnetic environment, passive detection systems pose serious threats and challenges to the radar's living environment. The radio frequency stealth technology refers to a stealth technology of active electronic equipment such as radars and the like for resisting interception, sorting, identification and tracking of an enemy passive detection system, aims at reducing the interception distance and the interception probability of the passive detection system on the radio frequency equipment such as the radars and the like, and can further improve the battlefield viability and the combat efficiency of the radars and the carrying platforms thereof. When the radar networking system detects the target, the total radiation power of the radar networking system is reduced under the condition that the target detection performance is not influenced, the radio frequency stealth performance of the system can be effectively improved, and the battlefield viability of the system is improved.

When a radar networking system working in the same frequency band is considered to perform target detection, how to reduce the total radiation power of the radar networking system under the condition of meeting certain target detection performance is a problem to be solved urgently in the prior art.

Disclosure of Invention

The invention provides a radar networking power control method based on a non-cooperative game, which is used for reducing the total radiation power of a radar networking system and improving the radio frequency stealth performance of the system under the condition of meeting certain target detection performance when the radar networking system working in the same frequency band is considered for target detection.

The invention adopts the following technical scheme for solving the technical problems:

a radar networking power control method based on a non-cooperative game comprises the following steps:

(1) acquiring channel propagation loss between each radar and a target in a radar networking system, wherein the mathematical description is as follows:

wherein,for the transmit antenna gain of the ith radar,for the receive antenna gain of the ith radar,is radar cross section of target relative to ith radar, lambda is radar emission signal wavelength, R_iIs the distance between the ith radar and the target, N_tThe number of radars in the system;

(2) sounding range according to specified SINRWherein:for the lower limit of the signal to interference plus noise ratio (SINR) value,establishing a radar networking power control model based on a non-cooperative game for the upper limit of the SINR value:

wherein s.t. denotes that the optimization objective function is "limited" by the following constraint, u_i(p_i,p_-i) As a utility function of radar i, p_iIs the transmission power value, p, of radar i_-iRepresenting the radiated power of all other radars in the system except radar i, b_iIn order to be a penalty factor,representing the maximum radiated power of radar i, the SINR gamma of the ith radar_iCan be represented by the following formula:

wherein, c_i,jRepresenting the cross-correlation coefficient, σ, between radar i and radar j²Is the system noise power, p_jIs the transmission power value of the radar j,representing the propagation loss of the channel between radar i and radar j, d_i,jRepresents the distance between radar i and radar j, b_iAs a penalty factor whenWhen b is greater than_iIs kept unchanged whenWhen the temperature of the water is higher than the set temperature,when in useWhen the temperature of the water is higher than the set temperature,

(3) will utility function u_i(p_i,p_-i) For radiation power p_iCalculating a first partial derivative:

wherein: u. of_i(p_i,p_-i) Is the utility function of radar i;

(4) by makingThe iterative expression of the radiation power of each radar in the radar networking system is obtained as follows:

wherein:for the nth iteratively calculated radar i transmission power value,the radar i transmission power value calculated for the (n + 1) th iteration,and calculating the radar i signal-to-noise ratio value for the nth iteration.

The invention has the following beneficial effects:

the invention not only reduces the interference among different radars in the radar networking system, but also improves the radio frequency stealth performance of the system under the condition of meeting certain target detection performance.

Drawings

FIG. 1 is a flow chart of the present invention.

Detailed Description

The invention is described in further detail below with reference to the accompanying drawings.

1. Determining the channel propagation loss and the target RCS (Radar Cross Section):

the invention provides a radar networking power control method based on a non-cooperative game. The method utilizes the propagation loss between each radar and the target and the prior knowledge of the RCS of the target relative to each radar, so the propagation loss between each radar and the target and the RCS of the target relative to each radar are determined firstly. A model of a radar networking system operating in the same frequency band is assumed as shown in fig. 1.

2. Determining parameters such as radiation parameters and target detection SINR (Signal-to-Interference-plus-Noise Ratio) range of a radar networking system:

according to the requirement of radio frequency stealth performance, the gain of a transmitting antenna and the gain of a receiving antenna of the ith radar in a radar networking system are respectively assumed to beHaving a maximum radiation power ofAdditive white Gaussian noise power at radar receiver is σ²A target sounding SINR range calculated from the specified SINRWherein:for the lower limit of the signal to interference plus noise ratio (SINR) value,is the upper limit of the SINR value.

3. Constructing a radar networking power control model of a non-cooperative game, and determining a range meeting target detection SINRMinimum total transmitted power ofExpression (c):

according to the requirement of a radar networking system on target detection performance, a mathematical model of radar networking power control based on a non-cooperative game is established, and the mathematical model is as follows:

in the formula, s.t. represents that the optimization objective function is "limited" by the following constraint, u_i(p_i,p_-i) As a utility function of radar i, p_iIs the transmission power value, p, of radar i_-iRepresenting the radiated power of all other radars in the system except radar i,represents the maximum radiated power of the radar i,is the channel propagation loss between radar i and the target, wherein,for the transmit antenna gain of the ith radar,for the receive antenna gain of the ith radar,RCS of target relative to ith radar, lambda is radar emission signal wavelength, R_iThe distance between the ith radar and the target; n is a radical of_tThe number of radars in the system;wherein, c_i,jRepresenting the cross-correlation coefficient, σ, between radar i and radar j²Is the system noise power, p_jIs the transmission power value of the radar j,representing the propagation loss of the channel between radar i and radar j, d_i,jRepresents the distance between radar i and radar j, b_iAs a penalty factor whenWhen b is greater than_iIs kept unchanged whenWhen the temperature of the water is higher than the set temperature,when in useWhen the temperature of the water is higher than the set temperature,

4. will utility function u_i(p_i,p_-i) For radiation power p_iThe first partial derivative is taken and made equal to zero:

for determining the transmission power of each radarThe utility function u in the formula (1)_i(p_i,p_-i) For radiation power p_iThe first partial derivative is taken and made equal to zero as follows:

5. designing solvable nonlinear equationsNewton iterative algorithm of (1):

by solving the equation (2), the radiation power of each radar can be obtainedThe iterative expression is:

wherein:for the nth iteratively calculated radar i transmission power value,the radar i transmission power value calculated for the (n + 1) th iteration,calculating the signal-to-noise ratio of the radar i for the nth iteration; through iterative calculation, the range satisfying the target detection SINR is obtainedAnd a group of radiation power distribution results for minimizing total radiation power of the radar networking systemAnd finally determining the total radiation power of the system as an optimal solution, wherein the obtained radiation power value of each radar is the radar networking power distribution result with the radio frequency stealth performance.

Claims (1)

1. A radar networking power control method based on a non-cooperative game is characterized by comprising the following steps:

(1) acquiring channel propagation loss between each radar and a target in a radar networking system, wherein the mathematical description is as follows:

$h_{i,i}=\frac{G_i^t{G}_i^r{\mathrm{\σ}}_i^{RCS}{\mathrm{\λ}}^2}{{\left(4\mathrm{\π}\right)}^3{R}_i^4},i=1,2,...,N_t$

wherein,for the transmit antenna gain of the ith radar,for the receive antenna gain of the ith radar,is radar cross section of target relative to ith radar, lambda is radar emission signal wavelength, R_iIs the distance between the ith radar and the target, N_tThe number of radars in the system;

(2) sounding range according to specified SINRWherein:for the lower limit of the signal to interference plus noise ratio (SINR) value,establishing a radar networking power control model based on a non-cooperative game for the upper limit of the SINR value:

$\left\{\begin{array}{cc}\underset{\left\{p_i,i=1,\mathrm{...},N_t\right\}}{\max }& u_i\left(p_i,p_{-i}\right)=\arctan \left(1+{\mathrm{\γ}}_i\right)+b_i{h}_{i,i}\ln \left(p_i^{\max }-p_i\right),\\ s.t.:& {\mathrm{\γ}}_{th}^{\min }\≤{\mathrm{\γ}}_i\≤{\mathrm{\γ}}_{th}^{\max },i=1,\mathrm{...},N_t\\ & 0\≤p_i\≤p_i^{\max },i=1,\mathrm{...},N_t\end{array}\right.$

wherein s.t. denotes that the optimization objective function is "limited" by the following constraint, u_i(p_i,p_-i) As a utility function of radar i, p_iIs the transmission power value, p, of radar i_-iRepresenting the radiated power of all other radars in the system except radar i, b_iIn order to be a penalty factor,representing the maximum radiated power of radar i, the SINR gamma of the ith radar_iCan be represented by the following formula:

${\mathrm{\γ}}_i=\frac{h_{i,i}{p}_i}{\underset{j=1,j\≠i}{\overset{N_t}{\Σ}}{c}_{i,j}{h}_{i,j}{p}_j+{\mathrm{\σ}}^2},i=1,2,...,N_t$

wherein, c_i,jRepresenting the cross-correlation coefficient, σ, between radar i and radar j²Is the system noise power, p_jIs the transmission power value of the radar j,representing the propagation loss of the channel between radar i and radar j, d_i,jRepresents the distance between radar i and radar j, b_iAs a penalty factor whenWhen b is greater than_iIs kept unchanged whenWhen the temperature of the water is higher than the set temperature,when in useWhen the temperature of the water is higher than the set temperature,

(3) will utility function u_i(p_i,p_-i) For radiation power p_iCalculating a first partial derivative:

$\frac{\∂u_i\left(p_i,p_{-i}\right)}{\∂p_i}=\frac{h_{i,i}}{\underset{j=1,j\≠i}{\overset{N_t}{\mathrm{\Σ}}}{c}_{i,j}{h}_{i,j}{p}_j+{\mathrm{\σ}}^2}\frac{1}{1+{\left(1+{\mathrm{\γ}}_i\right)}^2}-\frac{b_i{h}_{i,i}}{p_i^{\max }-p_i}$

wherein: u. of_i(p_i,p_-i) Is the utility function of radar i;

(4) by makingThe iterative expression of the radiation power of each radar in the radar networking system is obtained as follows:

$p_i^{\left(n+1\right)}=\left\{\begin{array}{cc}\sqrt{\frac{p_i^{\max }-p_i}{b_i{h}_{i,j}}\frac{p_i^{\left(n\right)}}{{\mathrm{\&gamma;}}_i^{\left(n\right)}}-{\left(\frac{p_i^{\left(n\right)}}{{\mathrm{\&gamma;}}_i^{\left(n\right)}}\right)}^2}-\frac{p_i^{\left(n\right)}}{{\mathrm{\&gamma;}}_i^{\left(n\right)}},& 0<p_i^{\left(n+1\right)}<p_i^{\max }\\ p_i^{\max },& p_i^{\left(n+1\right)}\&GreaterEqual;p_i^{\max }\end{array}\right.$

wherein:for the nth iteratively calculated radar i transmission power value,the radar i transmission power value calculated for the (n + 1) th iteration,and calculating the radar i signal-to-noise ratio value for the nth iteration.